Olshanskii S. Solution of problems in variable mass spherical body dynamics

The object of investigation is the motion of a homogeneous spherical body size variables, which can rotate in a gaseous environment. The purpose and objectives of the study: the purpose of research is to develop a mathematical model of homogeneous spherical body mass change is associated with an increase or decrease its radius and to find analytical solutions to the problems. Methods of research adopted in the complex are exact and approximate analytical methods of the theory of differential equations. Scientific novelty of the results: a mathematical model and analytical method of solving nonlinear differential equations with variable coefficients in the Bessel functions, which describes the vertical motion of a spherical body of variable size and mass, with a quadratic dependence of the aerodynamic force on the speed of flight discovered nonmonotonic flight speed and the conditions for existence extremum of the velocity of vertical motion of a spherical body. The practical significance of the results: the results can be used in assessing the speed and range of fire extinguishing agents, taking into account the convective flow. According to the results of the research was obtained in the act of introducing the research work of the Institute of Mechanical Engineering. A.N. Podgorny: "Development of simulation algorithm of power function for analysis of associated loads on the elements of space payload with the spacecraft," Spectrum-UF.